Abstract Rifting can result in asymmetric conjugate margins. In numerical models with laterally homogeneous lithosphere, the polarity of the asymmetry is random and results from spontaneous strain localization on a dominant fault/shear zone. However, along the central South Atlantic, margin width is well correlated to the proximity of the rift to a craton during rifting. To understand the evolution of rifting close to a craton, we used numerical experiments that included a thick craton lithosphere adjacent to a thinner, mobile-belt lithosphere. When rifting starts close to the craton, i.e., ≤ 100 km, deformation focuses along a fault/shear zone dipping toward the craton, leading to cratonward asymmetric asthenospheric uplift and rift migration. This results in a narrow margin on the craton side and a wide margin on the mobile-belt side. Craton-related asymmetry results in the wide margin subsiding more than the narrow one, inducing the formation of large synrift sag basins in the wide conjugate, as in the South Atlantic. This differential subsidence is preserved for ~100 m.y. after breakup and may partly explain the present-day higher dynamic topography close to cratons in the central South Atlantic. Mantle flow during asymmetric rifting leads to weakening of the craton lithosphere, partial intermixing, and recycling into the convective mantle, as interpreted for this sector of the South Atlantic ridge. Thus, rifting adjacent to a craton may have wide-ranging tectonic, stratigraphic, and compositional consequences that affect not only margin architecture, but also the development of subsequent dynamic topography and the spreading system.